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Company X has 2 million shares of common stock outstanding at a book value of $1...

Company X has 2 million shares of common stock outstanding at a book value of $1 per share. The stock is currently priced at $5.00 per share. The company also has $2 million in face value of debt, with exactly 15 years remaining until maturity and a coupon rate of 10% paid semiannually. The yield to maturity on the bonds is 12%.

What is the weight of debt capital to be used in calculating the firm’s weighted average cost of capital (WACC)?

A) 14.71%

B) 15.30%

C) 46.30%

D) 50.00%

Expert Solution

Step 1: Bond price calculation

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

note: It is general practice to take $1,000 as face value when no details are given.

Prima facie, the bond will trade at discount as YTM>coupon rate

Year	Cash flow	PVAF/PVF@6%	*Present Value (CashflowPVAF/PVF)**
1-30	50	13.7648*	688.24
30	1000	0.1741**	174.11

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 688.24+174.11

= $862.35

Note : Since the bond makes semiannual interest payments, total no. of period is 30 (15*2), cashflow per period is 50(1000*10%/2) and cashflows are discounted at 6% (12/2).

*PVAF = (1-(1+r)^-n)/r

**PVF=1/(1+r)^n

Weight of debt capital = Market Value of Debt/( Market Value of Equity+ Market Value of Debt/)

= ((2 million/1000)*862.35)/(((2 million/1000)*862.35)+(2 million*5))

= 1724700/(1724700+10000000)

= 1724700/11724700

= 14.71%

jeff jeffy answered 1 year ago

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